The paper presents in an applicative manner a parameter-based methodology about design, modeling and optimization of a spur gear pump, currently under production in a Romanian company. Wanting to expand their product range, the company asked for a parameter-based design of this type of pump, FEM simulations and optimization of its conception to cover a wider range of flow rates, as required by current beneficiaries. The purpose of this research was to find improved alternative solutions via parametric design, mathematical validation and finite element simulation of the manufacturing solutions. The pump model is well known and has been manufactured for decades in many countries, under various licenses and constructive variants. The research process analyzed the functional role of the gear pump, its structure, its 3D model, which was reconstructed from the last manufactured solution, while identifying certain dimensions to be optimized and used in parametric design relations. The author used the CATIA V5 software and Visual Basic programing language. By mathematical computation, there were identified the pressure values and forces generated in the pump’s gears, applied later in FEM simulations to check the behavior of the pump components at the loads generated by these forces and pressures. The paper identifies and presents in a summary table the maximum stress values, deformations and percentages of computation errors for each pump’s constructive solution.